MOS Multi-layer neural network and its design method

ABSTRACT

Disclosed is a multi-layer neural network and circuit design method. The multi-layer neural network receiving an m-bit input and generating an n-bit output comprises a neuron having a cascaded pair of CMOS inverters and having an output node of the preceding CMOS inverter among the pair of CMOS inverters as its inverted output node and an output node of the succeeding CMOS inverter as its non-inverted output node, an input layer having m neurons to receive the m-bit input, an output layer having n neurons to generate the n-bit output, at least one hidden layer provided with n neurons to transfer the input received from the input layer to the directly upper hidden layer or the output layer, an input synapse group in a matrix having each predetermined weight value to connect each output of neurons on the input layer to each neuron of the output layer and at least one hidden layer, at least one transfer synapse group in a matrix having each predetermined weight value to connect each output of neurons of the hidden layer to each neuron of its directly upper hidden layer or of the output layer, and a bias synapse group for biasing each input node of neurons of the hidden layers and the output layer.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a MDS multi-layer neural network andits designing method, and more particularly to a multi-layer neuralnetwork and the designing method thereof which can easily realize VLSIcircuitry for a multi-layer neural network.

2. Description of the Related Art

Recently, in the pattern recognition field, neural networks which can dolarge-scale parallel processing in real-time have been introduced. In1988, Hans P. Graf et al. of Bell laboratories, presented a patternrecognizing neural network wherein amplifiers, having their inputs andoutputs interconnected through a resistive connecting device in amatrix, constitute synapses and neurons of the neural network, and apair of switches which switch according to the data in a pair of RAMcells, constitute neuron interconnections.

The present inventor has filed numerous applications including: an adder(U.S. application Ser. No. 07/473,653), a multiplier (07/473,633), anA/D converter (07/473,631, 07/473,634), a pattern classifier(07/473,464), etc. These related applications disclose a neural networkhaving synapses constructed using PMOS and/or NMOS transistors, andincluding neurons made from buffers in the form of cascaded pairs ofCMOS inverters. The aforementioned neural circuits are based on aone-layer neural network model and solve only linearly separableproblems, but not linearly unseparable problems (non-linear problems).Accordingly, their application is extremely limited. For instance, anXOR circuit cannot be properly modelled by a one-layer neural network.The limitations of one-layer neural networks are overcome by properlydesigned multi-layer neural networks. It is known that a neural networkcan learn by a back-propagation algorithm (refer to IEEE ASSP MAGAZINE,pages 4 to 22, April, 1987).

There are more restrictions, however, in the hardware implementation ofmulti-layer neural networks than in software simulated algorithms in acomputer. This is due to the fact that hardware implementation of amulti-layer neural network depends on current VLSI technology. As aresult, circuit implementation of connection weight values for neuralcircuits and non-linear functions is not as readily attainable as withsoftware simulated algorithms. Although real number calculations withfloating point operation and also neural network models requiringincreased interconnection capability can be achieved using software,such software implemented operations become difficult with VLSItechnology.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a multi-layer neuralnetwork having integer connecting weight values and a step function, tosolve the problem of the conventional technique.

It is another object of the present invention to provide a circuitdesign method of a multi-layer neural network for designing themulti-layer neural network according to the new learning rule.

To achieve the object, the multi-layer neural network of the presentinvention receiving an m-bit input and generating an n-bit outputcomprises:

a neuron for cascading a pair of CMOS inverters and having an outputnode of the preceding CMOS inverter among the pair of CMOS inverters asits inverted output node and an output node of the succeeding CMOSinverter as its non-inverted output node;

an input layer having m neurons to receive the m-bit input;

an output layer having n neurons to generate the n-bit output;

at least one hidden layer provided with n neurons to transfer the inputreceived from the input layer to the directly upper hidden layer or theoutput layer;

an input synapse group on a matrix having each predetermined weightvalue to connect each output of neurons on the input layer to eachneuron of the output layer and at least one hidden layer;

at least one transfer synapse group in a matrix having eachpredetermined weight-value to connect each output of neurons of thehidden layer to each neuron of its directly upper hidden layer or of theoutput layer; and

a bias synapse group for biasing each input node of neurons of thehidden layers and the output layer.

Here, the input synapse group, the transfer synapse group and the biassynapse group are constructed by PMOS and NMOS transistors.

There is also provided a method for designing the above describedmulti-layer neural network for receiving an m-bit input and generatingan n-bit output, which comprises:

a first step of initializing the connection weight value of the inputsynapse group;

a second step of setting the m-bit input value and an n-bit desiredoutput value corresponding to the input value;

a third step of obtaining the sum of the input weight values at theinput node of each neuron of the output layer and generating an actualoutput by a step function;

a fourth step of comparing the actual output value obtained in the thirdstep, with the desired output value set in the second step to calculatethe error, and storing the variation of the weight value calculatedaccording to the error value;

a fifth step of terminating the learning if each output value equals itsdesired output value, or if not, obtaining the sum of the storedvariation of the weight value and adding it to each current weight valueto obtain a new weight value, after the second step through the fourthstep are carried out with respect to 2^(m) input and output pairs;

a sixth step of reducing each weight value by a predetermined ratio,when the sum of the new weight value obtained in the fifth step in theinput node of each neuron of the output layer is above a predeterminedvalue; and

a seventh step of using the output layer as a hidden layer, incrementingthe new output layer, and repeating the process beginning with thesecond step using the output of the hidden layer and the original inputas new inputs, when the desired result is not obtained after repeatingthe learning upto the sixth step by the predetermined times ofrepetitions.

BRIEF DESCRIPTION OF THE DRAWINGS

The above objects and other advantages of the present invention willbecome more apparent by describing the preferred embodiment of thepresent invention with reference to the attached drawings, in which:

FIG. 1 is a concept diagram of a conventional multi-layer neuralnetwork;

FIG. 2 is a characteristic graphic diagram of a sigmoid function used inthe learning of the conventional multi-layer neural network;

FIG. 3 is a concept diagram of a multi-layer neural network according tothe present invention;

FIG. 4 is a characteristic graphic diagram of a step function used inthe learning of the multi-layer neural network according to the presentinvention;

FIG. 5A is a circuit diagram of an embodiment of the multi-layer neuralnetwork according to the present invention;

FIG. 5B is a partial circuit diagram for explaining the synapsestructure of FIG. 5A; and

FIG. 5C is a common transistor representation of each circle elementshown in bias synapse group S4 of FIG. 5A.

DETAILED DESCRIPTION OF THE INVENTION

Hereinafter, the present invention will be described with reference tothe accompanying drawings.

FIG. 1 is a concept diagram of a general multi-layer neural networkwhich is a feed forward network having nodes of at least one layerbetween input and output nodes. These additional layers include hiddenunits or nodes which are not directly connected to both the input andoutput nodes. As shown in FIG. 1, the three-layer neural network hastwo-layer hidden layers L1 and L2 between the input layer L0 and theoutput layer L3. The input layer L0 has five neuron units or nodes N01to N05 to receive inputs X₀ to X₄. The hidden layers L1 and L2 each havethree neuron units or nodes N11, N12, & N13, and N21, N22, & N23,respectively, while output layer L3 also has three neuron units or nodesN31, N32, and N33 to respectively generate outputs Y₀, Y₁, and Y₂. Here,it should be noted that the number of neuron units of each layer isdetermined by the number of input and output bits of the circuitry ofthe system. The neuron units or nodes of each layer are connected withall of the neuron units of its directly preceding lower layer only.

The conventional multi-layer neural network is learned by the previouslyknown back-propagation training algorithm (BPTA). The BPTA has thegraphic characteristic shown in FIG. 2 and uses the sigmoid functionrepresented in the following Eq. (I) ##EQU1##

However, since the sigmoid function is an exponential function, thehardware implementation is difficult and complicated.

Also, when a binary input and a step function are used, the conventionalmulti-layer neural network may have just one value with respect todifferent input values because of the connection structure betweenlayers. As a result, the upper layer input values cannot bediscriminated.

FIG. 3 is a concept view of a multi-layer neural network according tothe present invention. The present multi-layer neural network isdifferent from the multi-layer neural network of FIG. 1 in that theneuron units or nodes of each layer are connected with all neuron unitsof the immediate input layer as well as those of its directly precedinglower layer. Since other parts of this constitution is the same as thoseof FIG. 1, the same reference numerals will be used for thecorresponding parts. Also, the learning of the multi-layer neuralnetwork of the present invention has the graphic characteristic shown inFIG. 4 and uses the step function represented in the following Eq. (II):##EQU2## fh (ΣWi·Xi-θ): hard limit non-linear function θ: thresholdvalue of neuron node

Wi: connection weight value with respect to Xi

Xi: input

The circuit of multi-layer neural network according to the presentinvention is designed by the learning algorithm as follows.

Step 1: All connection weight values between nodes are initialized.

Step 2: A pair of input and desired output are presented to input andoutput. Here, the inputs are m-bit binary values and the total number ofinputs is 2^(m), and the outputs are n-bit binary values and the totalnumber of outputs is 2^(n). Accordingly, identical output values withrespect to different inputs can be obtained.

Step 3: The sum of the input weight values at each node is obtained andthe actual output is generated by the step function. Here, Eq. (II) isused for the step function.

Step 4: The desired output value at an output node is compared with theactual output value obtained in step 3, thereby calculating an error,and the variation of the weight value according to the error is stored.That is, the error δ is:

    δ=Desired Output-Actual Output

and the weight value variation ΔW is

    ΔW=δ×Input

Step 5: After steps 2, 3, and 4 are carried out for each input andoutput pair, if all the actual output values are equal to the desiredoutput values, the learning ends. If not, the total sum of the weightvalue variation ΔW is added to each weight value. That is, the newweight value (W_(T)) is:

    W.sub.T =W.sub.T-1 +ΣΔW

where T equals the number of learnings.

Step 6: When the sum of the new weight value W_(T) with respect to eachnode's input is above a determined value M, the weight values W_(T) arereduced at a predetermined rate. That is, the weight value W_(T) isreduced by the following equation: ##EQU3## assuming, ΣW_(T) >M andwhere W_(T) ' is the weight value obtained after the T learningprocesses have been conducted.

Step 7: If the preceding steps (from step 2) are repeated apredetermined number of times with a new weight value W_(T) and withoutreaching the desired result, the current output layer becomes a hiddenlayer, the new output layer is incremented, and then the process isrepeated (beginning at step 2) using the original input together withthe output of the directly preceding hidden layers as a new input to thenew output layer.

Hence, learning is performed by one-layer learning. If a desired outputvalue is correctly obtained, learning ends. However, if learning isrepeated a predetermined number of times, and the result remainsincorrect, then a layer is added. In the incremented new layer, theoriginal input and the incomplete actual output of directly followinghidden layers are used as new inputs. Learning is then repeated for thefollowing layer. At that point, an output layer associated with firstlearning step is changed to serve as a hidden layer. As a result, in thefollowing layer, the subsequent learning step is repeated as in thelearning step of the previous layer, but with more inputs by the numberof outputs of the directly lower hidden layer. During the learningprocess, whenever an input is added, the variation in weight value isstored. After all inputs are applied, the sum of variations of the totalweight values is added into the weight value, thereby making a newweight value.

Here, the sum of the weight value to be compared with one neuron isabove the predetermined value M, Eq. (II) is applied with respect toeach weight value to reduce them at a predetermined rate, therebylimiting the sum of the weight values to within the value M.

An embodiment of a multi-layer neuron network designed with respect tospecific inputs and outputs through such a learning, is shown in FIG.5A. As shown in FIG. 5A, the multi-layer neural network is embodied withCMOS inverters and PMOS and NMOS transistors. In FIG. 5A, a three-layerneuron network is shown having a 5-bit input and a 3-bit output. Thus,an input layer L0 has five neurons N01 to N05, and two hidden layers L1and L2 each including three neurons N11, N12, & N13, and N21, N22, &N23, respectively. Similarly, output layer L3 also has three neuronsN31, N32, and N33. Here, each neuron of every layer is a cascadedconnection of a pair of CMOS inverters INT1 and INT2 as shown in FIG.5B, and is constructed with a buffer where an output node of precedingCMOS inverter INT1 is an inverted output node NDB and the output node offollowing CMOS inverter INT2 is a non-inverted output node ND. Thesynapse for connecting each neuron of an input layer and each neuron ofoutput layer is constructed of PMOS and NMOS transistors by thefollowing method.

If the learning obtains a final connection weight which is positive, andthe input neuron IN receives a high logic signal (input bit value=1),the corresponding connection strength in the form of a first supplyvoltage (e.g., supply voltage Vcc) is connected to the input node IND ofthe output neuron ON through the PMOS transistor B whose gate is commonwith the inverted output node NDB, and for negative connection weightvalues, the connection is to a second supply voltage (e.g., ground orVss) through NMOS transistor C whose gate is common with thenon-inverted output node ND. Conversely, when the input neuron receivesa low (input bit value=0) and the connection weight is positive, theconnection strength is in the form of supply voltage Vcc connectedthrough PMOS transistor A whose gate is also common to the non-invertedoutput mode ND, while for negative weights, the connection strength is aground potential or equals the second supply voltage Vss, and isconnected through NMOS transistor D whose gate is tied to the invertedoutput node NDB.

If the connection weight value is "0", no connections are made,regardless of the logic state of the input bit.

Using this method, an input synapse group S1 and transfer synapse groupsS2 and S3 of FIG. 5A are constructed of PMOS and NMOS transistors. Here,each neuron of input layer L0 is connected to each input node of everyneuron of the two hidden layers L1 and L2 and output layer L3, throughthe aforesaid input synapse group S1 in a matrix. Each neuron of hiddenlayer L1 is connected to each input node of neuron of its directlyfollowing hidden layer L2 through the transfer synapse group S2 of thematrix. Similarly, each neuron of hidden layer L2 is connected to eachinput node of the neurons of output layer L3, through the transfersynapse group S3 in a matrix.

Also, all neuron input nodes of the two hidden layers L1 and L2 andoutput layer L3 shown in FIG. 5A are biased to the second supply voltageVss or GND through each bias synapse group S4. Since the bias synapsegroup S4 biases the input node of each neuron to the second supplyvoltage Vss or GND when the input is not applied and thus biases eachneuron output to "0", the bias synapse group S4 is composed of NMOStransistor, wherein the first supply voltage Vcc is supplied to thegate, the drain is connected to input node of each neuron, and thesecond supply voltage (Vss or GND) is connected to the source. Here, theNMOS transistor for a bias synapse has the geometric aspect ratio(channel width (W)/ channel length (L)) to have a connection strengthequivalent to the unit weight value. For instance, when the W/L ratio ofNMOS transistor is 2 μm/2 μm as a unit weight value, the W/L ratio ofthe PMOS transistor becomes 5 μm/2 μm. This is set considering themobility ratio of electron to hole, and each weight value is a multipleof the unit weight value; that number being an integer. Thus, the termof "+1" in Eq. (II) is a constant considering the bias synapse value.

The embodiment applying the multi-layer neural network of the presentinvention as described above to the 2-bit full adder and the sine wavegenerating circuit is as follows.

Embodiment I 2-bit Full Adder

When the maximum value M of the sum of weight values of each node is 20and 40, and the learning number is 300 and 500, the number of layers areas shown in Table 1 and the result is shown in List 1.

                  TABLE 1                                                         ______________________________________                                                    learning number                                                   M             300     500                                                     ______________________________________                                        20            4       4                                                       40            3       3                                                       ______________________________________                                    

Input file name is "a"

Connection type is 2

Max. weight sum=20

Number of learnings=300

Initial weight value=0

Max. weight is used

Displayed percent is a variable unit

Delta weight is uninitialized

    ______________________________________                                        input/output                                                                  ______________________________________                                        0 0 0 0 0    0 0 0                                                            0 0 0 0 1    0 0 1                                                            0 0 0 1 0    0 0 1                                                            0 0 0 1 1    0 1 0                                                            0 0 1 0 0    0 1 0                                                            0 0 1 0 1    0 1 1                                                            0 0 1 1 0    0 1 1                                                            0 0 1 1 1    1 0 0                                                            0 1 0 0 0    0 0 1                                                            0 1 0 0 1    0 1 0                                                            0 1 0 1 0    0 1 0                                                            0 1 0 1 1    0 1 1                                                            0 1 1 0 0    0 1 1                                                            0 1 1 0 1    1 0 0                                                            0 1 1 1 0    1 0 0                                                            0 1 1 1 1    1 0 1                                                            1 0 0 0 0    0 1 0                                                            1 0 0 0 1    0 1 1                                                            1 0 0 1 0    0 1 1                                                            1 0 0 1 1    1 0 0                                                            1 0 1 0 0    1 0 0                                                            1 0 1 0 1    1 0 1                                                            1 0 1 1 0    1 0 1                                                            1 0 1 1 1    1 1 0                                                            1 1 0 0 0    1 1 0                                                            1 1 0 0 1    1 0 0                                                            1 1 0 1 0    1 0 0                                                            1 1 0 1 1    1 0 1                                                            1 1 1 0 0    1 0 1                                                            1 1 1 0 1    1 1 0                                                            1 1 1 1 0    1 1 0                                                            1 1 1 1 1    1 1 1                                                            ______________________________________                                        (Error percentage)                                                            ______________________________________                                         3%  3% 15% 18% 25% 25% 21% 25% 25% 25% 25% 21% 28%                           25% 21% 21% 25% 21% 21% 28% 28% 25% 25% 21% 21% 25%                           25% 21% 25% 25% 21% 28% 28% 25% 21% 21% 21% 25% 25%                           21% 28% 25% 21% 21% 28% 25% 21% 21% 25% 21% 21% 28%                           28% 25% 25% 21% 21% 25% 25% 21% 25% 25% 21% 28% 28%                           25% 21% 21% 21% 25% 25% 21% 28% 25% 21% 21% 28% 25%                           21% 21% 25% 21% 21% 28% 28% 25% 25% 21% 21% 25% 25%                           21% 25% 25% 21% 28% 28% 25% 21% 21% 21% 25% 25% 21%                           28% 25% 21% 21% 28% 25% 21% 21% 25% 21% 21% 28% 28%                           25% 25% 21% 21% 25% 25% 21% 25% 25% 21% 28% 28% 25%                           21% 21% 21% 25% 25% 21% 28% 25% 21% 21% 28% 25% 21%                           21% 25% 21% 21% 28% 28% 25% 25% 21% 21% 25% 25% 21%                           25% 25% 21% 28% 28% 25% 21% 21% 21% 25% 25% 21% 28%                           25% 21% 21% 28% 25% 21% 21% 25% 21% 21% 28% 28% 25%                           25% 21% 21% 25% 25% 21% 25% 25% 21% 28% 28% 25% 21%                           21% 21% 25% 25% 21% 28% 25% 21% 21% 28% 25% 21% 21%                           25% 21% 21% 28% 28% 25% 25% 21% 21% 25% 25% 21% 25%                           25% 21% 28% 28% 25% 21% 21% 21% 25% 25% 21% 28% 25%                           21% 21% 28% 25% 21% 21% 25% 21% 21% 28% 28% 25% 25%                           21% 21% 25% 25% 21% 25% 25% 21% 28% 28% 25% 21% 21%                           21% 25% 25% 21% 28% 25% 21% 21% 28% 25% 21% 21% 25%                           21% 21% 28% 28% 25% 25% 21% 21% 25% 25% 21% 25% 25%                           21% 28% 28% 25% 21% 21% 21% 25% 25% 21% 28% 25% 21%                           21% 28%                                                                       ______________________________________                                        h.sub.-- value (actual output)                                                ______________________________________                                        0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         1 1 1                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         1 1 1                                                                         1 1 1                                                                         1 1 1                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 1 1                                                                         1 1 1                                                                         1 1 1                                                                         1 1 1                                                                         1 1 1                                                                         1 1 0                                                                         1 1 0                                                                         1 1 0                                                                         1 1 1                                                                         1 1 0                                                                         1 1 1                                                                         1 1 1                                                                         1 1 1                                                                         ______________________________________                                        layer number = 0                                                              ______________________________________                                         5  3 4 3 3                                                                    4  4 4 4 4         INPUT "1"                                                 -1 -1 5 5 5                                                                   ______________________________________                                        weight 2                                                                      ______________________________________                                        -8 -2 -6 -1 -1                                                                 4  4  4  4  4         INPUT "0"                                               6  6 -2 -2 -2                                                                ______________________________________                                        new input                                                                     ______________________________________                                        0 0 0 0 0 0 1 1                                                               0 0 0 0 1 0 1 1                                                               0 0 0 1 0 0 1 1                                                               0 0 0 1 1 0 1 1                                                               0 0 1 0 0 0 1 1                                                               0 0 1 0 1 0 1 1                                                               0 0 1 1 0 0 1 1                                                               0 0 1 1 1 1 1 1                                                               0 1 0 0 0 0 1 0                                                               0 1 0 0 1 0 1 1                                                               0 1 0 1 0 0 1 1                                                               0 1 0 1 1 0 1 1                                                               0 1 1 0 0 0 1 1                                                               0 1 1 0 1 1 1 1                                                               0 1 1 1 0 1 1 1                                                               0 1 1 1 1 1 1 1                                                               1 0 0 0 0 0 1 0                                                               1 0 0 0 1 0 1 1                                                               1 0 0 1 0 0 1 1                                                               1 0 0 1 1 1 1 1                                                               1 0 1 0 0 1 1 1                                                               1 0 1 0 1 1 1 1                                                               1 0 1 1 0 1 1 1                                                               1 0 1 1 1 1 1 1                                                               1 1 0 0 0 1 1 0                                                               1 1 0 0 1 1 1 0                                                               1 1 0 1 0 1 1 0                                                               1 1 0 1 1 1 1 1                                                               1 1 1 0 0 1 1 0                                                               1 1 1 0 1 1 1 1                                                               1 1 1 1 0 1 1 1                                                               1 1 1 1 1 1 1 1                                                               ______________________________________                                         3%  3% 25% 25% 25% 21% 37% 28% 31% 37% 43% 59% 46%                           46% 46% 28% 31% 34% 50% 53% 46% 43% 50% 71% 43% 31%                           50% 46% 46% 59% 53% 50% 68% 46% 46% 53% 40% 25% 34%                           46% 46% 56% 56% 40% 43% 53% 37% 28% 59% 59% 46% 53%                           56% 28% 28% 21% 28% 25% 40% 59% 53% 65% 34% 28% 46%                           59% 53% 53% 62% 46% 50% 59% 59% 43% 40% 68% 59% 62%                           59% 46% 50% 62% 59% 50% 50% 65% 56% 46% 56% 46% 46%                           59% 50% 46% 68% 59% 65% 46% 40% 43% 59% 50% 50% 56%                           56% 59% 50% 50% 68% 50% 59% 62% 50% 34% 25% 40% 50%                           59% 62% 71% 56% 53% 53% 46% 40% 37% 59% 50% 34% 56%                           59% 56% 28% 21% 34% 46% 62% 46% 50% 53% 50% 46% 46%                           46% 46% 46% 50% 53% 59% 53% 50% 50% 65% 50% 40% 50%                           59% 62% 59% 46% 50% 65% 59% 59% 34% 28% 25% 43% 50%                           56% 62% 50% 53% 65% 46% 46% 62% 59% 50% 53% 56% 43%                           31% 21% 50% 59% 56% 46% 34% 34% 40% 31% 43% 34% 68%                           50% 53% 59% 46% 53% 50% 62% 46% 53% 62% 59% 65% 43%                           43% 43% 50% 65% 62% 59% 68% 43% 50% 50% 53% 68% 25%                           28% 43% 71% 68% 71% 56% 50% 53% 56% 62% 62% 59% 68%                           62% 53% 46% 34% 46% 53% 46% 53% 59% 62% 46% 59% 59%                           53% 50% 31% 25% 53% 53% 50% 31% 28% 31% 43% 53% 62%                           56% 56% 31% 50% 46% 43% 46% 59% 68% 65% 56% 50% 43%                           43% 56% 46% 40% 56% 65% 31% 28% 31% 46% 46% 59% 62%                           50% 50% 43% 46% 62% 46% 50% 65% 46% 50% 59% 59% 68%                           50% 53%                                                                       ______________________________________                                        h.sub.-- value                                                                ______________________________________                                        0 0 0                                                                         0 1 0                                                                         0 1 0                                                                         0 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         0 1 0                                                                         0 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         1 0 0                                                                         1 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         1 0 0                                                                         1 1 0                                                                         1 1 0                                                                         1 1 0                                                                         1 0 0                                                                         1 0 0                                                                         1 0 0                                                                         1 1 0                                                                         1 1 0                                                                         1 1 0                                                                         1 1 0                                                                         1 1 1                                                                         ______________________________________                                        layer number = 1                                                              ______________________________________                                        4 2 3 2 2  3 0  0                                                             3 2 2 1 1 -5 1  2                                                             2 1 3 1 1 -6 1 -1                                                             ______________________________________                                        weight 2                                                                      ______________________________________                                        -5 -2 -3 -1 -1 -5 0 0                                                         -4 -2 -2 -1 -1  6 0 0                                                         -2 -2 -3 -2 -2  4 0 1                                                         ______________________________________                                        new point                                                                     ______________________________________                                        0 0 0 0 0 0 0 0                                                               0 0 0 0 1 0 1 0                                                               0 0 0 1 0 0 1 0                                                               0 0 0 1 1 0 1 0                                                               0 0 1 0 0 0 1 0                                                               0 0 1 0 1 0 1 1                                                               0 0 1 1 0 0 1 1                                                               0 0 1 1 1 1 0 0                                                               0 1 0 0 0 0 1 0                                                               0 1 0 0 1 0 1 0                                                               0 1 0 1 0 0 1 0                                                               0 1 0 1 1 0 1 1                                                               0 1 1 0 0 0 1 1                                                               0 1 1 0 1 1 0 0                                                               0 1 1 1 0 1 0 0                                                               0 1 1 1 1 1 1 0                                                               1 0 0 0 0 0 1 0                                                               1 0 0 0 1 0 1 1                                                               1 0 0 1 0 0 1 1                                                               1 0 0 1 1 1 0 0                                                               1 0 1 0 0 1 0 0                                                               1 0 1 0 1 1 1 0                                                               1 0 1 1 0 1 1 0                                                               1 0 1 1 1 1 1 0                                                               1 1 0 0 0 1 0 0                                                               1 1 0 0 1 1 0 0                                                               1 1 0 1 0 1 0 0                                                               1 1 0 1 1 1 1 0                                                               1 1 1 0 0 1 1 0                                                               1 1 1 0 1 1 1 0                                                               1 1 1 1 0 1 1 0                                                               1 1 1 1 1 1 1 1                                                               ______________________________________                                         3% 25% 46% 56% 46% 56% 62% 62% 56% 50% 50% 59% 62%                           65% 56% 62% 71% 56% 71% 65% 56% 40% 62% 56% 71% 71%                           62% 71% 56% 62% 71% 62% 71% 68% 56% 56% 71% 56% 71%                           71% 68% 59% 71% 71% 59% 62% 68% 68% 43% 65% 62% 50%                           71% 65% 71% 56% 71% 68% 56% 68% 71% 71% 71% 59% 71%                           65% 78% 71% 56% 71% 59% 50% 68% 62% 53% 25% 46% 71%                           68% 81% 65% 59% 68% 56% 71% 71% 68% 71% 71% 56% 71%                           78% 75% 71% 65% 71% 34% 31% 65% 71% 68% 68% 59% 59%                           78% 71% 40% 56% 68% 71% 71% 46% 25% 56% 71% 68% 65%                           71% 71% 71% 68% 62% 78% 59% 71% 68% 56% 68% 71% 59%                           46% 65% 71% 65% 71% 56% 71% 65% 65% 78% 68% 71% 65%                           68% 68% 65% 56% 71% 71% 71% 65% 71% 71% 71% 81% 81%                           71% 84% 87% 84% 96% 81% 62% 75% 90% 90% 84% 87% 93%                           71% 96% 87% 96% 96% 71% 96% 87% 96% 93% 78% 87% 93%                           84% 96% 87% 59% 84% 87% 90% 84% 87% 93% 71% 96% 87%                           96% 96% 71% 96% 87% 96% 93% 78% 87% 93% 84% 96% 87%                           59% 84% 87% 90% 84% 87% 93% 71% 96% 87% 96% 96% 71%                           96% 87% 96% 93% 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                                       0  0   0  0  0                                                               10  10  -5 -5 -5                                                             ______________________________________                                        new input                                                                     ______________________________________                                        0 0 0 0 0 0 1 1                                                               0 0 0 0 1 0 1 1                                                               0 0 0 1 0 0 1 1                                                               0 0 0 1 1 0 1 1                                                               0 0 1 0 0 0 1 1                                                               0 0 1 0 1 0 1 1                                                               0 0 1 1 0 0 1 1                                                               0 0 1 1 1 1 1 1             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1                                                               1 0 1 0 1 1 1 1                                                               1 0 1 1 0 1 1 1                                                               1 0 1 1 1 1 1 1                                                               1 1 0 0 0 1 1 0                                                               1 1 0 0 1 1 1 0                                                               1 1 0 1 0 1 1 0                                                               1 1 0 1 1 1 1 0                                                               1 1 1 0 0 1 1 0                                                               1 1 1 0 1 1 1 0                                                               1 1 1 1 0 1 1 0                                                               1 1 1 1 1 1 1 1                                                               ______________________________________                                         3%  3% 25% 40% 28% 37% 31% 34% 28% 37% 46% 46% 40%                           43% 46% 43% 50% 50% 50% 53% 46% 43% 56% 50% 62% 71%                           65% 56% 62% 62% 62% 62% 62% 46% 50% 40% 43% 40% 43%                           31% 46% 46% 53% 34% 53% 53% 28% 53% 56% 40% 40% 56%                           59% 53% 53% 53% 59% 56% 65% 53% 46% 65% 62% 62% 56%                           50% 34% 40% 46% 56% 56% 43% 50% 43% 59% 53% 50% 37%                           25% 46% 71% 65% 50% 46% 53% 59% 71% 43% 40% 68% 65%                           53% 25% 37% 71% 46% 50% 59% 50% 46% 34% 53% 50% 62%                           65% 59% 46% 59% 59% 53% 50% 56% 50% 53% 37% 40% 37%                           34% 28% 50% 56% 50% 56% 59% 68% 53% 50% 31% 50% 65%                           53% 56% 59% 46% 34% 68% 50% 31% 56% 65% 46% 53% 59%                           53% 25% 46% 65% 46% 56% 40% 62% 53% 62% 71% 59% 53%                           53% 50% 43% 65% 65% 62% 59% 50% 34% 31% 43% 65% 46%               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                                       0 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         0 0 1                                                                         0 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         1 0 0                                                                         1 0 1                     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 -7 -4 -6 -3 -3 -9 -1 -2                                                      -12 -6  0  0  0  13 -6  0                                                      -4 -2 -4 -1 -1  10  7 -8                                                     ______________________________________                                        recall                                                                        ______________________________________                                        0 0 0                                                                         0 0 1                                                                         0 0 1                                                                         0 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                            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                                   

Input file name is "a"

Connection type is 2

Max weight sum=40

Number of learnings=500

Initial weight value=0

Max weight is used

Displayed percent is a variable unit

Delta weight is uninitialized

    ______________________________________                                        0 0 0 0 0  0 0 0                                                              0 0 0 0 1  0 0 1                                                              0 0 0 1 0  0 0 1                                                              0 0 0 1 1  0 1 0                                                              0 0 1 0 0  0 1 0                                                              0 0 1 0 1  0 1 1                                                              0 0 1 1 0  0 1 1                                                              0 0 1 1 1  1 0 0                                                              0 1 0 0 0  0 0 1                                                              0 1 0 0 1  0 1 0                                                              0 1 0 1 0  0 1 0                                                              0 1 0 1 1  0 1 1                                             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                              1 1 0 0 1  1 0 0                                                              1 1 0 1 0  1 0 0                                                              1 1 0 1 1  1 0 1                                                              1 1 1 0 0  1 0 1                                                              1 1 1 0 1  1 1 0                                                              1 1 1 1 0  1 1 0                                                              1 1 1 1 1  1 1 1                                                               3%  3%  3% 28% 15% 25% 25% 25% 25% 25% 25% 15% 34%                           21% 25% 25% 18% 25% 21% 28% 28% 25% 25% 28% 28% 28%                           25% 21% 28% 25% 21% 21% 21% 21% 25% 28% 28% 25% 25%                           34% 28% 25% 25% 21% 28% 25% 28% 21% 25% 25% 25% 28%                           21% 25% 25% 28% 28% 21% 25% 21% 34% 25% 25% 28% 21%                           25% 21% 28% 28% 25% 25% 28% 28% 28% 25% 25% 28% 25%                           21% 21% 21% 25% 25% 28% 28% 25% 25% 34% 28% 25% 25%                           21% 21% 21% 25% 28% 21% 25% 25% 28% 31% 25% 25% 28%                           28% 21% 25% 21% 28% 25% 25% 28% 21% 25% 21% 28% 28%                           25% 25% 21% 34% 25% 25% 21% 21% 25% 25% 31% 21% 25%                           25% 28% 28% 25% 25% 28% 28% 25% 21% 21% 21% 21% 25%                           28% 28% 25% 25% 34% 28% 25% 25% 21% 28% 25% 28% 21%                           25% 25% 25% 28% 21% 25% 25% 28% 28% 21% 25% 21% 34%                           25% 25% 28% 21% 25% 21% 28% 28% 25% 25% 28% 28% 28%                           25% 25% 28% 25% 21% 21% 21% 25% 25% 28% 28% 25% 25%                           34% 28% 25% 25% 21% 21% 21% 25% 28% 21% 25% 25% 28%                           31% 25% 25% 28% 28% 21% 25% 21% 28% 25% 25% 28% 21%                           25% 21% 28% 28% 25% 25% 21% 34% 25% 25% 21% 21% 25%                           25% 31% 21% 25% 25% 28% 28% 25% 25% 28% 28% 25% 21%                           21% 21% 21% 25% 28% 28% 25% 25% 34% 28% 25% 25% 21%                           28% 25% 28% 21% 25% 25% 25% 28% 21% 25% 25% 28% 28%                           21% 25% 21% 34% 25% 25% 28% 21% 25% 21% 28% 28% 25%                           25% 28% 28% 28% 25% 25% 28% 25% 21% 21% 21% 25% 25%                           28% 28% 25% 25% 34% 28% 25% 25% 21% 21% 21% 25% 28%                           21% 25% 25% 28% 31% 25% 25% 28% 28% 21% 25% 21% 28%                           25% 25% 28% 21% 25% 21% 28% 28% 25% 25% 21% 34% 25%                           25% 21% 21% 25% 25% 31% 21% 25% 25% 28% 28% 25% 25%                           28% 28% 25% 21% 21% 21% 21% 25% 28% 28% 25% 25% 34%                           28% 25% 25% 21% 28% 25% 28% 21% 25% 25% 25% 28% 21%                           25% 25% 28% 28% 21% 25% 21% 34% 25% 25% 28% 21% 25%                           21% 28% 28% 25% 25% 28% 28% 28% 25% 25% 28% 25% 21%                           21% 21% 25% 25% 28% 28% 25% 25% 34% 28% 25% 25% 21%                           21% 21% 25% 28% 21% 25% 25% 28% 31% 25% 25% 28% 28%                           21% 25% 21% 28% 25% 25% 28% 21% 25% 21% 28% 28% 25%                           25% 21% 34% 25% 25% 21% 21% 25% 25% 31% 21% 25% 25%                           28% 28% 25% 25% 28% 28% 25% 21% 21% 21% 21% 25% 28%                           28% 25% 25% 34% 28% 25% 25% 21% 28% 25% 28% 21% 25%                           25% 25% 28% 21% 25% 25% 28% 28% 21% 25% 21% 34% 25%                           25% 28% 21% 25% 21% 28% 28%                                                   ______________________________________                                        h.sub.-- value                                                                ______________________________________                                        0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         1 1 1                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         1 1 1                                                                         1 1 1                                                                         1 1 1                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 1 1                                                                         1 1 1                                                                         1 1 1                                                                         1 1 1                                                                         1 1 1                                                                         1 1 0                                                                         1 1 0                                                                         1 1 0                                                                         1 1 0                                                                         1 1 0                                                                         1 1 0                                                                         1 1 0                                                                         1 1 1                                                                         ______________________________________                                        layer number = 0                                                              ______________________________________                                         9  7 8 7 7                                                                    0  0 0 0 0                                                                   -8 -8 8 8 8                                                                   ______________________________________                                        weight 2                                                                      ______________________________________                                        -20 -2 -16  0  0                                                                0  0   0  0  0                                                               10  10  -5 -5 -5                                                             ______________________________________                                        new input                                                                     ______________________________________                                        0 0 0 0 0 0 1 1                                                               0 0 0 0 1 0 1 1                                                               0 0 0 1 0 0 1 1                                                               0 0 0 1 1 0 1 1                                                               0 0 1 0 0 0 1 1                                                               0 0 1 0 1 0 1 1                                                               0 0 1 1 0 0 1 1                                                               0 0 1 1 1 1 1 1                                                               0 1 0 0 0 0 1 0                                                               0 1 0 0 1 0 1 1                                                               0 1 0 1 0 0 1 1                                                               0 1 0 1 1 0 1 1                                                               0 1 1 0 0 0 1 1                                                               0 1 1 0 1 1 1 1                                                               0 1 1 1 0 1 1 1                                                               0 1 1 1 1 1 1 1                                                               1 0 0 0 0 0 1 0                                                               1 0 0 0 1 0 1 1                                                               1 0 0 1 0 0 1 1                                                               1 0 0 1 1 1 1 1                                                               1 0 1 0 0 1 1 1                                                               1 0 1 0 1 1 1 1                                                               1 0 1 1 0 1 1 1                                                               1 0 1 1 1 1 1 1                                                               1 1 0 0 0 1 1 0                                                               1 1 0 0 1 1 1 0                                                               1 1 0 1 0 1 1 0                                                               1 1 0 1 1 1 1 0                                                               1 1 1 0 0 1 1 0                                                               1 1 1 0 1 1 1 0                                                               1 1 1 1 0 1 1 0                                                               1 1 1 1 1 1 1 1                                                                3%  3% 21% 34% 28% 40% 25% 34% 25% 46% 40% 50% 34%                           46% 59% 53% 65% 62% 59% 37% 34% 31% 50% 59% 62% 59%                           53% 50% 46% 59% 53% 46% 62% 62% 50% 50% 46% 46% 50%                           53% 46% 43% 59% 37% 25% 59% 46% 46% 53% 50% 59% 46%                           43% 37% 43% 28% 50% 65% 40% 50% 56% 59% 53% 43% 53%                           59% 71% 65% 68% 71% 46% 40% 53% 53% 56% 62% 46% 46%                           34% 37% 40% 59% 53% 59% 62% 59% 50% 46% 53% 46% 53%                           62% 50% 53% 50% 50% 50% 53% 65% 50% 31% 56% 56% 65%                           62% 56% 56% 56% 53% 71% 53% 53% 50% 56% 50% 56% 37%                           40% 50% 59% 46% 50% 53% 59% 53% 25% 43% 62% 50% 59%                           56% 53% 46% 46% 50% 62% 56% 50% 50% 46% 50% 46% 50%                           46% 59% 62% 53% 40% 34% 40% 56% 59% 65% 50% 40% 50%                           50% 56% 43% 46% 53% 53% 50% 40% 50% 37% 53% 62% 62%                           59% 62% 62% 56% 56% 50% 40% 40% 37% 37% 62% 28% 34%                           59% 53% 37% 31% 59% 59% 68% 71% 56% 62% 59% 59% 50%                           34% 53% 62% 59% 50% 46% 53% 68% 43% 50% 56% 68% 53%                           53% 59% 71% 56% 62% 40% 43% 37% 68% 59% 50% 43% 34%                           50% 50% 62% 56% 43% 53% 56% 50% 50% 53% 56% 56% 59%                           56% 59% 34% 56% 56% 43% 37% 25% 37% 46% 56% 59% 59%                           65% 56% 46% 53% 46% 31% 37% 25% 37% 53% 71% 56% 59%                           62% 62% 59% 68% 53% 46% 46% 59% 43% 37% 59% 46% 46%                           62% 43% 53% 56% 50% 59% 40% 46% 43% 50% 46% 56% 50%                           62% 62% 43% 43% 40% 65% 62% 40% 53% 43% 46% 43% 40%                           31% 43% 59% 62% 53% 43% 50% 56% 65% 56% 53% 65% 62%                           43% 40% 50% 56% 62% 56% 53% 53% 65% 50% 50% 34% 40%                           53% 62% 56% 56% 37% 50% 71% 43% 46% 56% 65% 40% 43%                           31% 46% 50% 43% 50% 50% 56% 46% 68% 46% 71% 50% 34%                           46% 37% 43% 50% 65% 53% 50% 37% 28% 40% 46% 46% 59%                           25% 37% 65% 31% 56% 65% 43% 40% 25% 46% 65% 62% 65%                           62% 46% 50% 53% 56% 65% 56% 43% 25% 34% 40% 59% 56%                           46% 53% 46% 56% 46% 59% 62% 40% 68% 46% 46% 50% 56%                           43% 46% 56% 46% 25% 37% 37% 56% 65% 56% 62% 59% 50%                           53% 65% 56% 59% 62% 59% 56% 56% 53% 68% 46% 37% 37%                           31% 50% 59% 53% 50% 62% 50% 65% 50% 43% 46% 56% 53%                           59% 62% 65% 59% 56% 65% 53% 25% 34% 53% 68% 68% 59%                           75% 53% 53% 46% 28% 34% 59% 56% 50% 46% 50% 43% 50%                           62% 46% 43% 25% 50% 65% 62% 62% 68% 65% 68% 59% 46%                           50% 53% 53% 53% 56% 46% 40% 62% 40% 65% 50% 62% 62%                           68% 53% 40% 59% 65% 53% 37%                                                   ______________________________________                                        h.sub.-- value                                                                ______________________________________                                        0 0 0                                                                         0 0 0                                                                         0 0 0                                                                         0 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         0 0 0                                                                         0 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         1 0 0                                                                         1 0 1                                                                         0 1 1                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         1 0 0                                                                         1 0 1                                                                         1 0 1                                                                         1 1 1                                                                         1 0 0                                                                         1 0 0                                                                         1 0 0                                                                         1 0 1                                                                         1 0 1                                                                         1 1 1                                                                         1 1 1                                                                         1 1 1                                                                         ______________________________________                                        layer number = 1                                                              ______________________________________                                        8 6 7 5 5   4  0 -1                                                           8 4 1 0 0 -12  4  5                                                           6 5 5 5 5  -3 -4 -5                                                           ______________________________________                                        weight 2                                                                      ______________________________________                                        -8 -4 -7 -2 -2 -13 0  0                                                       -9 -6 -5 -3 -3  11 0  0                                                       -8 -3 -6  0  0  12 0 -5                                                       ______________________________________                                        new input                                                                     ______________________________________                                        0 0 0 0 0 0 0 0                                                               0 0 0 0 1 0 0 0                                                               0 0 0 1 0 0 0 0                                                               0 0 0 1 1 0 1 0                                                               0 0 1 0 0 0 1 0                                                               0 0 1 0 1 0 1 1                                                               0 0 1 1 0 0 1 1                                                               0 0 1 1 1 1 0 0                                                               0 1 0 0 0 0 0 0                                                               0 1 0 0 1 0 1 0                                                               0 1 0 1 0 0 1 0                                                               0 1 0 1 1 0 1 1                                                               0 1 1 0 0 0 1 1                                                               0 1 1 0 1 1 0 0                                                               0 1 1 1 0 1 0 0                                                               0 1 1 1 1 1 0 1                                                               1 0 0 0 0 0 1 1                                                               1 0 0 0 1 0 1 1                                                               1 0 0 1 0 0 1 1                                                               1 0 0 1 1 1 0 0                                                               1 0 1 0 0 1 0 0                                                               1 0 1 0 1 1 0 1                                                               1 0 1 1 0 1 0 1                                                               1 0 1 1 1 1 1 1                                                               1 1 0 0 0 1 0 0                                                               1 1 0 0 1 1 0 0                                                               1 1 0 1 0 1 0 0                                                               1 1 0 1 1 1 0 1                                                               1 1 1 0 0 1 0 1                                                               1 1 1 0 1 1 1 1                                                               1 1 1 1 0 1 1 1                                                               1 1 1 1 1 1 1 1                                                               ______________________________________                                         3% 28% 68% 59% 75% 71% 56% 71% 84% 78% 84% 93% 96%                           87% 93% 93% 90% 96% 96% 93% 96% 96% 87% 96% 96% 96%                           100%                                                                          ______________________________________                                        h.sub.-- value                                                                ______________________________________                                        0 0 0                                                                         0 0 1                                                                         0 0 1                                                                         0 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         0 0 1                                                                         0 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         1 0 0                                                                         1 0 1                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         1 0 0                                                                         1 0 1                                                                         1 0 1                                                                         1 1 0                                                                         1 1 0                                                                         1 0 0                                                                         1 0 0                                                                         1 0 1                                                                         1 0 1                                                                         1 1 0                                                                         1 1 0                                                                         1 1 1                                                                         ______________________________________                                        layer number = 2                                                              ______________________________________                                        7 4  6  3  3  5 -5 -4                                                         9 3 -1 -1 -1 -8  11  0                                                        2 4  3  4  4 -8 -9  2                                                         ______________________________________                                        weight 2                                                                      ______________________________________                                         -7 -4 -6 -3 -3 -10 -1  -1                                                    -11 -6  0  0  0  10 -6   2                                                      1 -2 -1 -2 -2   6  9 -13                                                    ______________________________________                                        recall                                                                        ______________________________________                                        0 0 0                                                                         0 0 1                                                                         0 0 1                                                                         0 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         0 0 1                                                                         0 1 0                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         1 0 0                                                                         1 0 1                                                                         0 1 0                                                                         0 1 1                                                                         0 1 1                                                                         1 0 0                                                                         1 0 0                                                                         1 0 1                                                                         1 0 1                                                                         1 1 0                                                                         1 1 0                                                                         1 0 0                                                                         1 0 0                                                                         1 0 1                                                                         1 0 1                                                                         1 1 0                                                                         1 1 0                                                                         1 1 1                                                                         ______________________________________                                    

EMBODIMENT II A circuit for generating a sine curve

The number of layers is shown in table 2 in the same condition as theembodiment I, and the results are shown in List II.

                  TABLE 2                                                         ______________________________________                                        M learning number   300    500                                                ______________________________________                                        20                  4      4                                                  40                  3      2                                                  ______________________________________                                    

List II

Input file name is "s"

Connection type is 2

Max. weight sum=20

Number of learnings=300

Initial weight value=0

Max. weight is used

Displayed percent is a variable unit

Delta weight is uninitialized

    __________________________________________________________________________    input/output                                                                             0 0 0 0                                                                           0 0 0 0                                                                   0 0 0 1                                                                           0 0 1 1                                                                   0 0 1 0                                                                           0 1 0 1                                                                   0 0 1 1                                                                           1 0 0 0                                                                   0 1 0 0                                                                           1 0 1 0                                                                   0 1 0 1                                           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Input file name is "s"

Connection type is 2

Max. weight sum=20

Number of learnings=500

Initial weight value=0

Max weight is used

Displayed percent is a variable unit

Delta weight is uninitialized

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                               0 0 1 1                                                                       0 1 0 1                                                                       1 0 0 0                                                                       1 0 1 0                                                                       1 0 1 1                                                                       1 1 0 1                                                                       1 1 1 1                                                                       1 1 1 1                                                                       1 1 1 1                                                                       layer number = 2                                                              4        4   4   4   0   0   0   0                                            6        1   4   -1  0   5   0   0                                            3        2   -4  3   1   0   3   0                                            3        0   -3  1   1   5   0   3                                            weight 2                                                                      0        0   0   0   -10 1   -2  3                                            -5       -1  -3  1   -1  -5  0   -1                                           -3       -2  3   -3  -1  0   -3  0                                            -4       0   4   -1  0   -4  1   -1                                           new input                                                                     0 0 0 0 0 0 0 0                                                               0 0 0 1 0 0 1 1                                                               0 0 1 0 0 1 0 1                                                               0 0 1 1 1 0 0 0                                                               0 1 0 0 1 0 1 0                                                               0 1 0 1 1 0 1 1                                                               0 1 1 0 1 1 0 1                                                               0 1 1 1 1 1 1 1                                                               1 0 0 0 1 1 1 1                                                               1 0 0 1 1 1 1 1                                                               20%                                                                              10%                                                                              60%                                                                              90%                                                                              90%                                                                              90%                                                                              90%                                                                              90%                                                                              90%                                                                              90%                                                                              100%                                            h.sub.-- value                                                                0 0 0 0                                                                       0 0 1 1                                                                       0 1 0 1                                                                       1 0 0 0                                                                       1 0 1 0                                                                       1 0 1 1                                                                       1 1 0 1                                                                       1 1 1 0                                                                       1 1 1 1                                                                       1 1 1 1                                                                       layer number = 3                                                              4        4   4   4   0   0   0   0                                            5        0   4   -1  0   6   -1  0                                            2        2   -4  3   0   0   4   0                                            3        -1  -4  0   0   3   -1  4                                            weight 2                                                                      -1       -1  0   0   -10 0   -2  3                                            -4       -1  -3  0   -1  -5  0   -1                                           -3       -3  2   -3  -1  0   -4  0                                            -3       0   4   0   1   -2  2   -3                                           recall                                                                        0 0 0 0                                                                       0 0 1 1                                                                       0 1 0 1                                                                       1 0 0 0                                                                       1 0 1 0                                                                       1 0 1 1                                                                       1 1 0 1                                                                       1 1 1 0                                                                       1 1 1 1                                                                       1 1 1 1                                                                       __________________________________________________________________________

Input file name is "s"

Connection type is 2

Max. weight sum=40

Number of learnings=300

Initial weight value=0

Max. weight is used

Displayed percent is a variable unit

Delta weight is uninitialized

    ______________________________________                                        0 0 0 0    0 0 0 0                                                            0 0 0 1    0 0 1 1                                                            0 0 1 0    0 1 0 1                                                            0 0 1 1    1 0 0 0                                                            0 1 0 0    1 0 1 0                                                            0 1 0 1    1 0 1 1                                                            0 1 1 0    1 1 0 1                                                            0 1 1 1    1 1 1 0                                                            1 0 0 0    1 1 1 1                                                            1 0 0 1    1 1 1 1                                                            ______________________________________                                        20% 10% 10% 30% 30% 50% 30% 30% 40% 40% 40% 30% 50%                           50% 50% 50% 50% 50% 50% 50% 50% 50% 60% 50% 20% 50%                           50% 50% 40% 40% 50% 50% 30% 30% 30% 50% 60% 40% 40%                           40% 50% 50% 40% 30% 20% 60% 60% 40% 40% 30% 50% 50%                           30% 30% 30% 60% 60% 40% 40% 40% 50% 30% 30% 30% 60%                           40% 40% 40% 60% 60% 30% 20% 40% 50% 50% 40% 40% 60%                           60% 40% 30% 50% 50% 40% 40% 40% 60% 40% 30% 30% 60%                           50% 50% 50% 50% 50% 50% 50% 50% 60% 50% 60% 60% 40%                           60% 60% 50% 40% 50% 50% 50% 40% 40% 60% 50% 40% 30%                           40% 40% 40% 50% 50% 40% 50% 50% 40% 30% 60% 70% 60%                           40% 30% 60% 60% 40% 30% 50% 50% 60% 50% 30% 30% 50%                           50% 60% 60% 30% 20% 30% 60% 40% 40% 50% 40% 40% 50%                           60% 50% 60% 60% 50% 50% 60% 70% 60% 30% 50% 50% 60%                           60% 70% 40% 50% 50% 60% 50% 60% 50% 50% 40% 60% 60%                           70% 60% 60% 50% 70% 60% 60% 50% 60% 60% 70% 60% 60%                           40% 50% 50% 50% 60% 60% 60% 70% 50% 50% 50% 50% 60%                           60% 60% 60% 50% 60% 60% 50% 70% 60% 60% 60% 50% 50%                           50% 70% 60% 70% 70% 50% 60% 70% 50% 60% 60% 40% 50%                           60% 40% 60% 60% 60% 60% 70% 70% 60% 60% 60% 50% 50%                           50% 60% 60% 50% 60% 60% 60% 60% 60% 60% 60% 60% 50%                           60% 50% 50% 50% 60% 50% 60% 60% 60% 60% 60% 60% 60%                           60% 60% 60% 60% 50% 50% 60% 60% 40% 40% 50% 50% 40%                           40% 60% 40% 50% 60% 60% 60% 50% 50% 50% 50% 40% 60%                           50% 50%                                                                       ______________________________________                                        h.sub.-- value                                                                ______________________________________                                        0 0 0 0                                                                       0 0 1 1                                                                       0 1 0 0                                                                       1 0 0 0                                                                       1 0 1 0                                                                       1 0 1 0                                                                       1 1 0 0                                                                       1 1 1 0                                                                       1 1 1 1                                                                       1 1 1 1                                                                       ______________________________________                                        layer number = 0                                                              ______________________________________                                        10  9  9 10                                                                   18  8  12  0                                                                  10 10 -8 10                                                                   20  4  4  9                                                                   ______________________________________                                        weight 2                                                                      ______________________________________                                        -10 -8  5  4                                                                  -19  0 -6  14                                                                  -9 -9  14 -6                                                                 -20  6  6  4                                                                  ______________________________________                                        new input                                                                     ______________________________________                                        0 0 0 0 0 0 0 0                                                               0 0 0 1 0 0 1 1                                                               0 0 1 0 0 1 0 0                                                               0 0 1 1 1 0 0 0                                                               0 1 0 0 1 0 1 0                                                               0 1 0 1 1 0 1 0                                                               0 1 1 0 1 1 0 0                                                               0 1 1 1 1 1 1 0                                                               1 0 0 0 1 1 1 1                                                               1 0 0 1 1 1 1 1                                                               ______________________________________                                        20% 20% 30% 50% 60% 70% 60% 60% 70% 60% 60% 70% 80%                           70% 60% 70% 80% 90% 70% 80% 80% 80% 80% 80% 80% 80%                           70% 80% 60% 80% 70% 80% 60% 80% 80% 80% 70% 80% 80%                           80% 70% 80% 90% 90% 80% 90% 90% 90% 90% 80% 80% 90%                           90% 80% 80% 80% 70% 80% 80% 70% 80% 80% 90% 80% 70%                           80% 90% 70% 80% 80% 80% 80% 90% 90% 80% 80% 90% 90%                           80% 80% 90% 80% 80% 80% 80% 80% 80% 70% 80% 70% 70%                           80% 80% 90% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80% 80%                           80% 80%                                                                       ______________________________________                                        h.sub.-- value                                                                ______________________________________                                        0 0 0 0                                                                       0 0 1 1                                                                       0 1 0 1                                                                       1 0 0 0                                                                       1 0 1 0                                                                       1 0 1 1                                                                       1 1 0 1                                                                       1 1 1 1                                                                       1 1 1 1                                                                       1 1 1 1                                                                       ______________________________________                                        layer number = 1                                                              ______________________________________                                         9 9  9 9 0 0  0 0                                                            13 5  11 0 0 8  0 0                                                            7 9 -4 7 2 0  6 1                                                             8 7  0 6 0 4 -6 5                                                            ______________________________________                                        weight 2                                                                      ______________________________________                                         -3 -6  0  3 -18   0 -1   6                                                   -10  0 -6  10   0 -10  0   0                                                   -4 -7  14 -5  -1   0 -6   0                                                    0  0  11  0  -1  -8  7 -10                                                  ______________________________________                                        new input                                                                     ______________________________________                                        0 0 0 0 0 0 0 0                                                               0 0 0 1 0 0 1 1                                                               0 0 1 0 0 1 0 1                                                               0 0 1 1 1 0 0 0                                                               0 1 0 0 1 0 1 0                                                               0 1 0 1 1 0 1 1                                                               0 1 1 0 1 1 0 1                                                               0 1 1 1 1 1 1 1                                                               1 0 0 0 1 1 1 1                                                               1 0 0 1 1 1 1 1                                                               ______________________________________                                        20% 30% 70% 90% 90% 90% 100%                                                  ______________________________________                                        h.sub.-- value                                                                ______________________________________                                        0 0 0 0                                                                       0 0 1 1                                                                       0 1 0 1                                                                       1 0 0 0                                                                       1 0 1 0                                                                       1 0 1 1                                                                       1 1 0 1                                                                       1 1 1 0                                                                       1 1 1 1                                                                       1 1 1 1                                                                       ______________________________________                                        layer number = 2                                                              ______________________________________                                         9 9  9  9  1  0  0 0                                                         13 3  10 -1  0  10 -1 0                                                        7 8 -8  7  1 -1  7 0                                                          9 0 -5  2 -2  2 -6 9                                                         ______________________________________                                        weight 2                                                                      ______________________________________                                        -6 -8 -1  0 -15  -2 -4   1                                                    -9 -1 -7  3  -2 -11 -1  -3                                                    -6 -7  7 -6  -3  -1 -8  -2                                                    -4  3  10  0   0  -4  4 -11                                                   ______________________________________                                        recall                                                                        ______________________________________                                        0 0 0 0                                                                       0 0 1 1                                                                       0 1 0 1                                                                       1 0 0 0                                                                       1 0 1 0                                                                       1 0 1 1                                                                       1 1 0 1                                                                       1 1 1 0                                                                       1 1 1 1                                                                       1 1 1 1                                                                       ______________________________________                                    

Input file name is "s"

Connection type is 2

Max. weight sum=40

Number of learnings=500

Initial weight value=0

Max. weight is used

Displayed percent is a variable unit

Delta weight is uninitialized

    ______________________________________                                        0 0 0 0    0 0 0 0                                                            0 0 0 1    0 0 1 1                                                            0 0 1 0    0 1 0 1                                                            0 0 1 1    1 0 0 0                                                            0 1 0 0    1 0 1 0                                                            0 1 0 1    1 0 1 1                                                            0 1 1 0    1 1 0 1                                                            0 1 1 1    1 1 1 0                                                            1 0 0 0    1 1 1 1                                                            1 0 0 1    1 1 1 1                                                            ______________________________________                                        20% 10% 10% 30% 30% 50% 30% 30% 40% 40% 40% 30% 50%                           50% 50% 50% 50% 50% 50% 50% 50% 50% 60% 50% 20% 50%                           50% 50% 40% 40% 50% 50% 30% 30% 30% 50% 60% 40% 40%                           40% 50% 50% 40% 30% 20% 60% 60% 40% 40% 30% 50% 50%                           30% 30% 30% 60% 60% 40% 40% 40% 50% 30% 30% 30% 60%                           40% 40% 40% 60% 60% 30% 20% 40% 50% 50% 40% 40% 60%                           60% 40% 30% 50% 50% 40% 40% 40% 60% 40% 30% 30% 60%                           50% 50% 50% 50% 50% 50% 50% 50% 60% 50% 60% 60% 40%                           60% 60% 50% 40% 50% 50% 50% 40% 40% 60% 50% 40% 30%                           40% 40% 40% 50% 50% 40% 50% 50% 40% 30% 60% 70% 60%                           40% 30% 60% 60% 40% 30% 50% 50% 60% 50% 30% 30% 50%                           50% 60% 60% 30% 20% 30% 60% 40% 40% 50% 40% 40% 50%                           60% 50% 60% 60% 50% 50% 60% 70% 60% 30% 50% 50% 60%                           60% 70% 40% 50% 50% 60% 50% 60% 50% 50% 40% 60% 60%                           70% 60% 60% 50% 70% 60% 60% 50% 60% 60% 70% 60% 60%                           40% 50% 50% 50% 60% 60% 60% 70% 50% 50% 50% 50% 60%                           60% 60% 60% 50% 60% 60% 50% 70% 60% 60% 60% 50% 50%                           50% 70% 60% 70% 70% 50% 60% 70% 50% 60% 60% 40% 50%                           60% 40% 60% 60% 60% 60% 70% 70% 60% 60% 60% 50% 50%                           50% 60% 60% 50% 60% 60% 60% 60% 60% 60% 60% 60% 50%                           60% 50% 50% 50% 60% 50% 60% 60% 60% 60% 60% 60% 60%                           60% 60% 60% 60% 50% 50% 60% 60% 40% 40% 50% 50% 40%                           40% 60% 40% 50% 60% 60% 60% 50% 50% 50% 50% 40% 60%                           50% 50% 40% 60% 40% 40% 60% 50% 50% 50% 60% 60% 50%                           60% 60% 50% 60% 50% 50% 40% 60% 60% 50% 50% 50% 50%                           50% 50% 60% 60% 60% 60% 60% 50% 50% 50% 50% 60% 60%                           60% 40% 70% 60% 60% 60% 60% 50% 50% 60% 60% 70% 50%                           50% 50% 50% 50% 50% 50% 60% 60% 60% 50% 50% 50% 50%                           60% 60% 60% 60% 60% 60% 60% 60% 60% 60% 60% 60% 60%                           60% 40% 60% 50% 50% 40% 60% 40% 50% 40% 40% 40% 60%                           40% 40% 50% 50% 40% 30% 50% 50% 40% 50% 60% 40% 50%                           50% 50% 50% 50% 50% 70% 60% 50% 40% 50% 60% 40% 50%                           60% 50% 40% 40% 60% 50% 50% 50% 60% 50% 30% 60% 50%                           50% 50% 50% 50% 60% 50% 50% 60% 50% 60% 60% 60% 40%                           60% 60% 50% 50% 60% 50% 50% 60% 50% 60% 50% 50% 60%                           60% 60% 60% 60% 60% 60% 60% 60% 60% 60% 60% 60% 60%                           60% 60% 60% 60% 50% 60% 50% 50% 40% 60% 60% 50% 40%                           60% 60% 40% 60% 60% 50% 60% 50% 60% 60% 60% 60% 50%                           60% 70% 60% 50% 60% 50% 50%                                                   ______________________________________                                        h.sub.-- value                                                                ______________________________________                                        0 0 0 0                                                                       0 0 1 1                                                                       0 1 0 1                                                                       0 0 0 1                                                                       1 0 1 1                                                                       1 0 1 1                                                                       1 1 0 1                                                                       1 1 1 1                                                                       1 1 1 1                                                                       1 1 1 1                                                                       ______________________________________                                        layer number = 0                                                              ______________________________________                                         9 10  9 10                                                                   18  8  12  0                                                                  10 10 -8 10                                                                   15  8  8  8                                                                   ______________________________________                                        weight 2                                                                      ______________________________________                                          1 -21  8  7                                                                 -19   0 -6  14                                                                 -9  -9  14 -6                                                                -20   6  6  6                                                                 ______________________________________                                        new input                                                                     ______________________________________                                        0 0 0 0 0 0 0 0                                                               0 0 0 1 0 0 1 1                                                               0 0 1 0 0 1 0 1                                                               0 0 1 1 0 0 0 1                                                               0 1 0 0 1 0 1 1                                                               0 1 0 1 1 0 1 1                                                               0 1 1 0 1 1 0 1                                                               0 1 1 1 1 1 1 1                                                               1 0 0 0 1 1 1 1                                                               1 0 0 1 1 1 1 1                                                               ______________________________________                                        20% 10% 40% 50% 30% 70% 40% 60% 60% 80% 60% 70% 80%                           70% 90% 80% 80% 80% 100%                                                      ______________________________________                                        h.sub.-- value                                                                ______________________________________                                        0 0 0 0                                                                       0 0 1 1                                                                       0 1 0 1                                                                       1 0 0 0                                                                       1 0 1 0                                                                       1 0 1 1                                                                       1 1 0 1                                                                       1 1 1 0                                                                       1 1 1 1                                                                       1 1 1 1                                                                       ______________________________________                                        layer number = 1                                                              ______________________________________                                         9 10  9 9  0 0  0 0                                                          12  5  10 0  1 7  0 1                                                          8  8 -6 6  2 0  5 1                                                          14  0 -3 5 -3 2 -6 4                                                          ______________________________________                                        weight 2                                                                      ______________________________________                                        -4 -8  0  4 -8   4  4 -4                                                      -8  0 -6  9 -2 -10  0 -1                                                      -5 -6  12 -5 -3   0 -5 -1                                                      0  5  8  2 -3  -8 -1 -9                                                      ______________________________________                                        recall                                                                        ______________________________________                                        0 0 0 0                                                                       0 0 1 1                                                                       0 1 0 1                                                                       1 0 0 0                                                                       1 0 1 0                                                                       1 0 1 1                                                                       1 1 0 1                                                                       1 1 1 0                                                                       1 1 1 1                                                                       1 1 1 1                                                                       ______________________________________                                    

What is claimed is:
 1. A MOS multi-layer neutral network receiving anm-bit input and generating an n-bit output, said neural networkcomprising:an input layer having m neurons each selectively arranged toreceive a corresponding bit value of said m-bit input, each neuronincluding first and second serially coupled CMOS inverters, an outputfrom each first CMOS inverter being connected to an input of acorresponding second CMOS inverter to generate a non-inverted outputtherefrom, said output from each first CMOS inverter also providing aninverted output associated with each neuron; an input synapse grouphaving a plurality of transistor synapse means coupled to respectiveones of said inverted and non-inverted outputs from said input layer toform a transistor group matrix, said transistor synapse means generatinga plurality of output row bias signals, each transistor synapse meansbeing assigned a predetermined weight value (current driving strength)in relation to its position along the transistor group matrix, each rowin the transistor group matrix being responsive to a respective biassignal pre-assigned to provide a select unity weight value bias signalonto said each row and also being responsive to a sum bias signal fromeach of said transistor synapse means respectively coupled thereto anddriven by corresponding ones of said inverted and non-inverted outputs,wherein each row is associated with one of said output row bias signalsgenerated in response to the selected unity weight value bias signal andthe respective sum bias signal coupled thereto; an output layer having nneurons each selectively arranged to output a corresponding bit value ofsaid n-bit output; at least one hidden layer, each coupled in successionbetween said input layer and said output layer and including n neurons,wherein a first hidden layer of said at least one hidden layers couplesfirst preselected n output row bias signals from said input synapsegroup to respective ones of its corresponding n neurons; and at leastone transfer synapse group, each associated with a corresponding one ofsaid at least one hidden layers and providing respective n first outputrow bias signals, each transfer synapse group having a plurality oftransfer synapse means coupled to corresponding ones of inverted andnon-inverted outputs from said respective n neurons and further coupledto second preselected n output row bias signals from said input synapsegroup to form a transfer group matrix for generating said respectivefirst n output row bias signals, each transfer synapse means beingassigned a predetermined weight value as a function of its positionalong the respective transfer group matrix, wherein each row in arespective transfer group matrix is coupled to either a correspondingone of the n neurons of each successive said at least one transfersynapse group or, if said respective transfer synapse group is the lastin succession, then to corresponding inputs of said n neurons of saidoutput layer, and wherein said input synapse group couples a supplyvoltage to each neuron of said output layer and said at least one hiddenlayer such that when a corresponding bit value into an input layerneuron is "1", then when a connection weight value is selected to bepositive, a first supply voltage is connected with a connection strengthof a corresponding connection weight value through a PMOS transistorwhose gate is connected to each corresponding inverted output, and whena connection weight value is selected to be negative, a second supplyvoltage is connected instead through an NMOS transistor whose gate isconnected to each corresponding non-inverted output, when acorresponding bit value into said input layer is "0", then when aconnection weight value is selected to be positive, a first supplyvoltage is connected with a connection strength of a correspondingconnection weight value through a PMOS transistor whose gate isconnected to each corresponding non-inverted output, and when aconnection weight value is selected to be negative, a second supplyvoltage is connected instead through an NMOS transistor whose gate isconnected to each corresponding inverted output, and when said input bitvalue is "1" or "0" and a connection weight value is "0," nothing isconnected, and wherein each transfer synapse group is composed of PMOSand NMOS transistors for connecting inverted and non-inverted neuronoutputs associated therewith.
 2. The MOS multi-layer neural network ofclaim 1, further comprising a bias synapse group for generating therespective bias signals preassigned to each input synapse group row toprovide a select unity weight value bias signal, each bias signal beinggenerated by an NMOS transistor whose gate is connected to said firstsupply voltage.
 3. The MOS multi-layer neural network of claim 2,wherein a connection weight value is a function of a geometric aspectratio of the respective MOS transistor (channel width/channel length).4. The MOS multi-layer neural network of claim 1, wherein a connectionweight value is an integer value.
 5. The MOS multi-layer neural networkof claim 1, wherein both the sum of connection weight values at eachoutput layer neuron input ad the sum of connection weight values at eachhidden layer neuron input is smaller than a fan-in value of a precedingstage neuron CMOS inverter.